• ON THE ANNIHILATOR GRAPH OF A COMMUTATIVE Γ- NEAR – RING

R. RAJESWARI*, N. MEENAKUMARI, T. TAMIZH CHELVAM

Abstract


Let M be a Commutative  near – ring with non zero identity. Let Z(M) be the set of all zero – divisors of M. For , let . We define the annihilator graph of M ,denoted by AG(M) ,as the  undirected graph whose set of vertices is Z  and two distinct vertices x and y are adjacent if and only if  .In this paper we study the ring theoretic properties of M and graph theoretic properties of .


Keywords


Annihilator graph, diameter, girth, zero – divisor graph.

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